// SPDX-License-Identifier: MIT
// Generated by EML-lang Solidity backend
// Source module: pid_controller
// Source file:   /home/monogate/monogate/forge/examples/pid_controller.eml
// Functions:     1 (1 @verify-annotated)
// Constants:     5
// WARNING: 3 fractional Real literal(s) were rounded to int256 (e.g. 0.6108 -> 1).
// For fixed-point semantics, scale your EML constants
// by WAD (1e18) and override the transcendental stubs
// with PRBMath SD59x18 in a derived contract.

pragma solidity ^0.8.20;

contract PidController {
    int256 constant Kp = 2 /* 1.5 rounded; see header re fixed-point */;
    int256 constant Ki = 0 /* 0.4 rounded; see header re fixed-point */;
    int256 constant Kd = 0 /* 0.05 rounded; see header re fixed-point */;
    int256 constant OUT_MIN = (-1);
    int256 constant OUT_MAX = 1;

    /// @notice Formal proof: pid_output_clamped (MachLib). Compiled from EML-lang.
    /// @dev Pfaffian profile: chain_order=0, cost_class=p0-d4-w0-c0, drift_risk=LOW.
    /// @dev Gas estimate: ~314 gas (PRBMath SD59x18 overrides assumed; run forge gas-bench for the canonical signal).
    /// @param error error (int256)
    /// @param integral integral (int256)
    /// @param derivative derivative (int256)
    /// @dev ensures: (result >= OUT_MIN)
    /// @dev ensures: (result <= OUT_MAX)
    function pid(int256 error, int256 integral, int256 derivative) external pure returns (int256) {
        require(((error < 0 ? -error : error) <= 100), "pid: refinement violated on error: ((error < 0 ? -error : error) <= 100)");
        require(((integral < 0 ? -integral : integral) <= 100), "pid: refinement violated on integral: ((integral < 0 ? -integral : integral) <= 100)");
        require(((derivative < 0 ? -derivative : derivative) <= 100), "pid: refinement violated on derivative: ((derivative < 0 ? -derivative : derivative) <= 100)");
        int256 raw = (((Kp * error) + (Ki * integral)) + (Kd * derivative));
        return _clamp(raw, OUT_MIN, OUT_MAX);
    }

    /// @dev clamp helper -- min(max(x, lo), hi).
    function _clamp(int256 x, int256 lo, int256 hi) internal pure returns (int256) {
        if (x < lo) return lo;
        if (x > hi) return hi;
        return x;
    }

}